District residents have renewed optimism about the direction of the city after Mayor Adrian M. Fenty's first year in office, and most say they expect his takeover of the public schools to improve the system, according to a new Washington Post poll. But those polled were less impressed by Fenty's efforts to reduce crime and create housing for the poor.

Even as the local real estate market has slowed and the D.C. government has been rocked by a massive embezzlement scandal, 56 percent of residents surveyed said they believe the city is on the right course, a 14-point jump from a Post poll in July 2006, the final year for former mayor Anthony A. Williams (D). Yet confidence in the city continues to break sharply along racial and socioeconomic lines.

Overall, Fenty (D), who swept into office by winning every voting precinct last year, remains popular, with more than seven in 10 residents saying they approve of his performance. The mayor made the takeover of the troubled schools his administration's top priority, and, though residents continue to decry the state of the almost 50,000-student system, 68 percent said they believe that Fenty's being in charge will improve it.

But the poll also revealed that the mayor faces persistently deep gulfs of perception between blacks and whites, and rich and poor residents when it comes to the city's quality of life. While 74 percent of whites in the poll say D.C. is headed in the right direction, 45 percent of African Americans agree. And two-thirds of those living in more affluent Northwest Washington see the city on the right course, compared with less than half of those who live in Northeast and Southeast.

Black women were the most dissatisfied group, with 38 percent saying they are pleased with the city's direction.

There was not a large enough sample of Asians, Latinos or other ethnic groups to report results within those groups.

During the 2006 campaign, Fenty pledged not to leave disenfranchised residents behind, a complaint often lodged against his predecessor. In an interview Friday, the mayor said his goal is to "stay focused on getting the job done . . . everywhere in the city and for everyone."

But when asked whether he is focused specifically on addressing the gaps in perception based on race and socioeconomic status, Fenty said that would be a mistake. "The minute you treat people differently . . . that's when you run into a very unbalanced way to run a government," he said.

Fenty made his comments shortly after conducting an hour-long news conference to detail what he said was an inadequate response by the government to the plight of four girls allegedly killed by their mother in the Washington Highlands neighborhood of Southeast. The shocking case, discovered Wednesday, served as a reminder that the mayor, who grimly pledged to make sure city agencies would more aggressively work to ensure the well-being of troubled families, has significant challenges ahead.

This week, Fenty and his handpicked schools chancellor, Michelle A. Rhee, will face criticism from parents in a series of public hearings over proposed school closings set for this fall.

The poll of 1,000 randomly selected adults was conducted from Jan. 3 to 8, and has a margin of sampling error of plus or minus three percentage points. Education ranked as the biggest concern among 40 percent of residents, followed by public safety at 26 percent -- a flip of the order in July 2006, when the city was experiencing a spike in crime.

It's not uncommon for mayors to be most popular in their first years; Williams received a 77 percent approval rating in 2000, but that had dropped to 54 percent by 2006.